Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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54 views

Levelized cost of electricity, to calculate the absolute costs?

I'm doing my master thesis about the renewable energies. So my goal is to calculate how much it will cost to switch our fuel based energy generation to renewable energy generation. So my first thought ...
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1answer
268 views

Debt accumulation equation derivation: valid given that it rests on calculus and the time period is a year? (nowhere near infinitesimal?)

Above is an image of what I’m referring to. The top ‘rule of thumb’ is derived using calculus, and hence is only valid for infinitesimal changes in t. However, this equation is considered over the ...
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1answer
142 views

Understanding the Zellener-Revankar Production Function

I took out a book from my university library called Econometric Modelling with Time Series: Specification Estimation and Testing in an attempt to understand the importance of MLE in Econometrics. ...
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1answer
841 views

How was the CES production function derived?

The Constant Elasticity of Substitution production function is defined as: (Taken from Wikipedia) $$Q=F \boldsymbol{\cdot}\left(a\boldsymbol{\cdot}K^r+(1-a)\boldsymbol{\cdot}L^r \right)^{1\over{r}}$$...
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1answer
77 views

Utility Functions: Implying endless consumption?

Do utility functions imply that if a consumer's income infinite, his consumption should also be infinite? The reason why I'd think this is the case is based on my basic understanding of utility ...
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1answer
2k views

How to derive the Indirect Utility Function from the Marshallian Demand Function?

I have been trying to derive the indirect utility function $(V(p,y))$, where $p$ is price and $w$ is wage, given the Marshallian demand functions $x(p,y)$ with the help of Roy’s identity (the utility ...
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1answer
91 views

Is there any good textbook for theoretical economics mathematical modelling? [duplicate]

I am currently reading some theoretical economics books and, of course, many mathematical expressions appear. I kind of guess their meaning, but it takes a lot of time and, after all, my guesses are ...
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1answer
141 views

Karush-Kuhn-Tucker in infinite dimension

Does the Karush-Kuhn-Tucker theorem on sufficient conditions for optimality of a convex program apply in countable dimension? For precisions, see Definition 4.1.1 and Theorem 4.1.4 of this course. ...
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293 views

Does the envelope theorem hold at a corner solution?

Suppose we have the following production function: $$F(L,K)=\max_{L_K}H(L,L_K,K)=\max_{L_K}\left[(L-L_K+1)^\alpha(L_K+K)^{1-\alpha}\right]=(L-L_K^*+1)^\alpha(L_K^*+K)^{1-\alpha}$$ With the ...
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0answers
391 views

Second order condition for symmetric game

Denote by $i \in \{1, \ldots, n\}$ an economic agent. Let $\mathbf x \in \mathbb R^n$ denote a vector of actions and $x_i \in \mathbf x$ a typical element. Let further $f_i : \mathbb R^n \to \mathbb ...
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1answer
110 views

Variance of $\hat{\beta _0}$ in case of homoskedasticity

Stock and Watson express the variance of $\hat{\beta _0}$ like $\hat{\sigma }^2_\hat{\beta _0}=\frac{E({X_{i}}^{2})}{n\sigma _{X}^{2}}\sigma ^{2}$, but starting from variance of $\hat{\beta _1}=\frac{...
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2answers
64 views

How to model spendthrift behavior

First, I'll introduce the observation and then ask the question. I have a brother-in-law who has a quirk: given the same product and two prices for it in different stores, he's willing to pay the ...
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1answer
219 views

Envelope theorem for discrete choice sets?

If we have a function $$f(x)=\max_yg(x,y)$$ Then we can find the derivative $d/dx \ f(x)$ by realizing that $$(1): \quad \frac {\partial }{\partial y}g(x,y^*)=0$$ because of the first order ...
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1answer
434 views

mathematical marxian models

Ive been doing some superficial reading on Feldman-Mahalanobis Model and have been wondering what other equations and "brand name" models that have been prodouced by marxist economists? What other ...
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1answer
67 views

Why $v_i=(X_i-\mu _X)u_i$ is i.i.d?

I don't understand. Ok, we have $\beta_1-\hat{\beta }_1=\frac{\frac{1}{n}\sum_{i=1}^{n}v_i}{(\frac{n-1}{n}){s_{X}}^{2}}$. So, for the first OLS assumption results that $E(v_i)=E((X_i-\bar{X})u_i\...
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2answers
180 views

Unconstrained Optimization:Why is there no “profit style” function in consumer theory?

When being exposed to your equations for profit maximization you have an equation of: $$\pi=pf(x)-c(x)$$ with this you can solve for the optimal input(s) $x$ from the first order conditions and some ...
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1answer
2k views

intuition behind the blanchard kahn conditions?

In order for a DSGE model to have a unique solution, it is required to satisfy the Blanchard Kahn conditions. However, these conditions seem very abstract to me. Is there an intuition behind the ...
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0answers
125 views

Deriving a Best Response Function in Baik (1994)

I'm reading a game-theory related paper*, and I'm not following the derivation of some property of the best-response functions. Suppose I have two players $1$ and $2$, whose strategies are ...
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2answers
101 views

Does every allocation have a maximal Pareto-improvement?

Consider an economy with a finite number of goods and a finite quantity of each good. Each agent $i$ has a preference-relation $\succeq_i$ which is a total, reflexive and transitive relation over the ...
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64 views

Mathematically optimal age to begin drawing Social Security retirement benefits as a function of expected life span?

So, for most of us Americans, our official retirement age is 66 and we get 100% of our retirement benefits. If we delay retirement, that benefit increases by 8% each year (up to age 70) and if we ...
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1answer
77 views

Contest game: second order condition satisfied, but negative profits?

The following is taken from Nti (1999) Consider a 2 player game in which each exerts effort in attempt to win a prize. Let $V_1$ be player $1$'s valuation of the prize and let $V_2$ be player $2$'s ...
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1answer
158 views

Math in Melitz and Ottaviano (2008)

I am reading Melitz and Ottaviano (2008), but I find it hard to understand some math in the model. The preference is given by : , which implies a demand function: Then the paper says the "inverse ...
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1answer
276 views

What are directional derivatives used for in economics?

In a basic mathematics for economists course one is exposed to the concept of directional derviative. Recall that a directional derivative is defined as: $$\nabla f \frac{\mathbb{v}}{\|\mathbb{v}\|}$$...
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2answers
843 views

Transformation of Cobb Douglas Utility

So, I need to determine whether or not $u=x^{0.5}y^{0.5}$ exhibits the same preferences as $u'= log(x) + log (y)$. Any tricks I can use here? I've done the logarithmic transformation so that I now ...
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68 views

Good book/article that goes into depth about transversality conditions?

I know how to derive the transversality condition in simple models like the Ramsey model. However, I am looking to develop a deeper understanding of transversality conditions in more complex models. ...
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3answers
511 views

Multivariable Utility functions

For a highschool economics/mathematics interdisciplinary essay I will use the Lagrange multipliers and deriving formulas that find the maximum. Could some one maybe suggest any (utility) functions ...
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59 views

Deviating from Cournot-Nash

Suppose player $1$ and $2$ are playing a simultaneous move game where with continuous strategies $x_1$ and $x_2$. The Cournot equilibrium is $x_1^*,x_2^*$. The following diagram purports to show that ...
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5answers
4k views

Applications of Trig functions in Economics?

Are there any applications of trig functions (ie $\sin(x)$, $\cos(x)$,$\tan(x)$) in economics?
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1answer
84 views

Subgame Perfect Equilibrium in Baye, Shin (1999)

The following is taken from Baye, Shin (1999) Consider a contest over a prize valued at 1 with symmetric players $1$ and $2$ who exert a level of effort $x_1$ and $x_2$ respectively. Effort cannot ...
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2answers
236 views

Envelope Theorem in Keen and Slemrod (2017)

This question pertains to the paper "Optimal Tax Administration" by Slemrod and Keen (2017). The IMF working paper is freely available on SSRN, however, it is not necessary to know the paper in order ...
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2answers
120 views

Intro to Modeling

I am "new" to economics but have some maths background (no analysis). Looking to learn how to read and make my own microeconomic models. Is there any online resources (or books) that can help me? I ...
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1answer
3k views

Homogenous of degree one in utility function.

Question My solution is as follows. Please check my solution. If I make a mistake, please tell. I am really not sure about my solution. Thank you U(x) is homogenous of degree one i.e. u(...
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60 views

How to econometrically identify perfect complements in production?

The production $$f(x_i,...,x_n)=\min\{x_i,...,x_n\}$$ is pretty straight forward and usually with smaller size data sets and can usually be picked up on rather quickly in an intuitive sense. ...
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4answers
2k views

Why is the Cobb-Douglas production function so popular?

As relatively novice quantitative analyst/ Cost analyst, Ive been asked to estimate the level of a given organizations productivity more than once, and then forecast for the next couple of periods. ...
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2answers
167 views

Use Brouwer's Fixed Point Theorem to Prove existence of equilibrium(a) with completely mixed strategies

How can one use Brouwer's Fixed Point Theorem to prove that the following game F has a solution: F is defined as N={L,R} Ai=(g,1-g) where g must be positive and smaller than 1, that is, each player ...
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0answers
99 views

What's the relation between deadweight-loss and alpha in Cobb-Douglas?

I'm studying for an exam and facing a question about the relationship between the $\alpha$ of the Cobb-Douglas function and the loss of utility of imposing taxes. If I have understood correctly, ...
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1answer
53 views

What does it mean when we say an iso curve has no interior?

From the paper: "Standard Auctions with Financially Constrained Bidders" - by Che and Gale. The authors describe an isobid curve as the curve that represents payments of the same value in a 2-...
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1answer
650 views

Solow growth model - analytic proof that Inada conditions imply steady state capital is increasing in the savings rate

Let's take the example of a generic Harrod-neutral (labor-augmenting) production function $f(k)$; all letters denote the growth rates they usually would. In the regular Solow growth model with the ...
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2answers
172 views

Is economics Turing Complete?

I am interested in economics from the perspective of mathematical physics and complexity theory. An important set of systems in complex systems are systems that are Turing Complete and are cases of ...
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0answers
127 views

Does a determinant ever have its own interpretation in economics?

I know there are applications of determinants in economics to compute equilibrium, aide in identifying profit maximisation/cost minimisation and in calculating elasticity of substitution. However, is ...
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1answer
224 views

Properties of preference relation

Let $\succeq$ be a preference relation on $X$. Is it true that $x \succeq y$ if and only if $\lnot (y \succ x)$? I think it is true and my proof is as follows. To prove $\implies$ direction, we have ...
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376 views

What does Sims' critique of economics models actually say?

I've been searching for answer, but I can't find a clear cut one. From what I understand it says that, in the realistic model there are no exogenous variables? Or does it say that there can be no ...
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1answer
476 views

What determines if a variable is exogenous or endogenous in a model? [duplicate]

Question above, I have a very rudimentary understanding of econometrics.
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1answer
2k views

What is Saddle Point Stability?

What is saddle point stability and what sorts of functions or systems of equations give rise to such a thing? For example, would we say that a two systems of stochastic difference equations that are ...
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1answer
202 views

Optimization: Dynamic Programming vs Kuhn-Tucker

Considering the standard utility maximization of representative household which lives forever, one may use dynamic programming and Kuhn-Tucker in case of discrete time. For instance, one would like to ...
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0answers
83 views

Visualising eigenvectors/values

This might seem like an odd question but seeing as I haven't had any formal education in solving ratex models yet, it is something I have been thinking about a lot recently. Consider the following ...
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2answers
85 views

Multidimensional screening and convexity of the surplus/rent function

I'm starting to read the literature of multidimensional screening models for monopolists selling $n$ goods to a continuum of buyers with $m=n$ dimensional types, and Rochet (1987) proves that a ...
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2answers
136 views

Budget hyperplane in n dimensions

Take the set of all vectors $x = (x_1, \cdots, x_n)$ that are solutions to $p_1x_1 + \cdots + p_nx_n = I > 0$. Show that this set has $n-1$ dimensions. I have somehow managed to get myself ...
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2answers
351 views

Quantitative Marxian/Marxist micro and macro economic models?

Are there quantitative Marxian/Marxist/neo-Marxist economic models like Dynamic Stochastic General Equilibrium models or Euro Area Wide (micro-founded) models - that can be used by central banks and ...
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1answer
48 views

Simplifying a monoplist's objective function under incomplete information

I am working through Rochet and Stohle (2003) chapter on multi-dimensional screening, and I am struggling filling in the blanks between equation (2.1) p. 154, and its simplified form on page 155. In ...